Hi,
In this shot, the camera is tilting down. If you look at the pic here, there's this little thing in the grass:
http://img27.picoodle.com/img/img27/3/10/18/f_Untitledm_d6f981f.jpg

I'd like to know of a technique someone can think of to make it invisible. I've tried color replacing, but had no luck. My only other idea is to create a transparent picture with a black dot on it, blur it, and put it on top of this clip's layer. But I'm not sure how I would get that picture moving upwards because the camera is tilting... moreover, the blur effect and other such effects don't seem to work on still png images like this.

You can deal with this is a similar way to blurring a face. Make a copy of the clip and place on top. Mask out a small area adjacent to the problem that is big enough to cover the blemish and feather the edges. Move the masked area to cover the problem.

If the camera is locked, you can do this with a small area of still overlay instead.

A tutorial for David J's method is found on Curt Wrigley's site:
http://www.wrigleyvideo.com/videotutorial/tut_premierepro.htm
Second tutorial down. Just substitute the concept of using a piece of the "good grass," for the Blur.

Derek,
You may well have the problem solved by now however another option that certainly saved my bacon when I had a similar problem was this fantastic tutorial >>>
http://maltaannon.com/articles/after-effects/simple-object-removal/
For even half decent editors it really opens your eyes, teaching you some great tricks.